What is the range of 1/(2x+4) ?

The range of 1/(2x+4) is f(x) 0

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range of 1/(2x+4)

range

\frac{1}{2 x + 4}

f (x) < 0 or f (x) > 0

Interval Notation

(- \infty, 0) \cup (0, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{1}{2 x + 4}

Inverse of

\frac{1}{2 x + 4} : \frac{1 - 4 x}{2 x}

\frac{1 - 4 x}{2 x}

Find the domain of each inverse function

Domain of

\frac{1 - 4 x}{2 x} : x < 0 or x > 0

Combine the intervals

f (x) < 0 or f (x) > 0

f (x) = (\frac{x - 2}{7})^{\frac{1}{3}}

f (x) = 36 x + \frac{9}{x}

f (x) = \frac{1}{x ^{2} - x - 90}

f (x) = \frac{( x - 1 )}{( x + 2 )}

f (x) = \frac{x + 7}{x ^{2} - x - 56}